Abstract

Using the recently developed theory of multiresolution decomposition, a self‐consistent formulation that governs the macroscale response of a linear dynamical system with nonstationary, microscale, stiffness heterogeneity is developed. The effects of the stiffness microstructure on the macroscale response are expressed via an across‐scales coupling operator that can be interpreted as an effective large‐scale measure of the material properties. It is shown that a stiffness microstructure can significantly affect a macroresponse. The effective properties are studied in the limit of a widely separated scales via general asymptotic considerations and specific numerical examples.